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We present the result for the three-loop singlet QCD corrections to the decayof a Higgs boson into two photons and improve the calculation for thenon-singlet case. With the new result presented, the decay width Gamma(H ->\gamma \gamma) is completely known at O(G_F \alpha ^2 \alpha_s^2, G_F \alpha^3).

Complete three-loop QCD corrections to the decay H -> \gamma \gamma